Investigation of eighth-grade students’ understanding of the slope of the linear function
Tipo de documento
Autores
Lista de autores
Birgin, Osman
Resumen
This study aimed to investigate eighth-grade students’ difficulties and misconceptions and their performance of translation between the different representation modes related to the slope of linear functions. The participants were 115 Turkish eighth-grade students in a city in the eastern part of the Black Sea region of Turkey. Data was collected with an instrument consisting of seven written questions and a semi-structured interview protocol conducted with six students. Students’ responses to questions were categorized and scored. Quantitative data was analyzed using the SPSS 17.0 statistical packet program with cross tables and one-way ANOVA. Qualitative data obtained from interviews was analyzed using descriptive analytical techniques. It was found that students’ performance in articulating the slope of the linear function using its algebraic representation form was higher than their performance in using transformation between graphical and algebraic representation forms. It was also determined that some of them had difficulties and misunderstood linear function equations, graphs, and slopes and could not comprehend the connection between slope and the x- and y-intercepts.
Fecha
2012
Tipo de fecha
Estado publicación
Términos clave
Comprensión | Dificultades | Funciones | Métodos estadísticos
Enfoque
Nivel educativo
Idioma
Revisado por pares
Formato del archivo
Volumen
26
Número
42a
Rango páginas (artículo)
139-162
ISSN
19804415
Referencias
ACUNA, C. Use of slope and y-intercept in prediction and description, as seen from students’ perspective. In: CONFERENCE OF THE EUROPEAN SOCIETY FOR RESEARCH IN MATHEMATICS EDUCATION, 3rd, 2007, Bellaria. Proceedings… Bellaria, Italy, 2007. BAKI, A. Bilgisayar destekli matematik . Ankara: Ceren . 2002. BAKI, A.; ÖZTEKIN, B. Teaching functions through Excel. Gazi University Kastamonu Education Journal, Turkey, v. 11, n. 2, p. 325 - 338. 2003. BARR, G. Graphs, gradients and intercepts. Mathematics in School, London, GB, v. 9, n. 1, p. 5 - 6. 1980. BELL, A.; JANVIER, C. The interpretation of graphs representing situations. For the Learning of Mathematics, Montreal, Canada, v. 2, n. 1, p. 34 - 42. 1981. BIRGIN, O.; KUTLUCA, T.; GÜRBÜZ, R. The effects of computer-assisted instruction on the students’ achievement in mathematics at seventh grade. In: INTERNATIONAL EDUCATIONAL TECHNOLOGY CONFERENCE 8th, 2008, Ankara. Proceedings…Ankara: Nobel Press. 2008. p. 879 – 882. CARPENTER, T. P.; CORBIT, M. K.; KEPNER, H. S.; LINDQUIST, M. M.; REYS, R. E.Results from the second mathematics assessment of the National Assessment of Educational Progress. Reston, VA: National Council of Teachers of Mathematics. 1981 CHIU, M. M.; KESSEL, C.; MOSCHKOVICH, J.; MUNOZ-NUNEZ, A. Learning tograph linear functions: a case study of conceptual change. Cognition and Instruction, Mahwah, NJ, v. 19, n. 2, p. 215 - 252. 2001. COHEN, J. A coefficient of agreement for nominal scales. Educational and Psychological Measurement, Durham, NC, v. 20, n. 1, p. 37 - 46. 1960 DAVIS, J. D. Real-world contexts, multiple representations, student-invented terminology, and Intercept. Mathematical Thinking and Learning, England, v. 9, n. 4, p. 387 - 418. 2007. EISENBURG, T. On the development of a sense for functions. In: HAREL, G.; DUBINSKY, E. (Eds.), The concept of function: Aspects of epistemology and pedagogy. Mathematical Association of America. 1992. p. 153 - 174, v. 25. GRAHAM, T.; SAHARP, J. An investigation into able students’ understanding of motion graphs. Teaching Mathematics and its Applications, Oxford, Inglaterra, v. 18, n. 3, p. 128 - 135. 1999. HITT, F. Difficulties in the articulation of different representations linked to the concept of function. Journal of Mathematical Behavior, Norwood, NJ, v. 17, n. 1, p. 123 - 134. 1998. ISIKSAL, M.; ASKAR, P. The effect of spreadsheet and dynamic geometry software on the achievement and self-efficacy of 7th grade students. Educational Research, Oxfordshire, Inglaterra, v. 47, n. 3, p. 333 - 350. 2005. JANVIER, C. Use of situations in mathematics education. Educational Studies in Mathematics, Dordrecht, Holanda, v. 12, p. 113 - 122. 1981. ,Ý.; GÜVEN B. The development of function concept in different levels of students. Eurasian Journal of Educational Research, Turkey, v. 16, p. 64 - 73. 2004. KERSLAKE, D. Graphs. In: HART, K. (Ed.), Children’s understanding of mathematics: 11-16. London: John Murray, 1981. p. 120 - 136. KNUTH, E. J. Student understanding of the Cartesian connection: an exploratory study. Journal for Research in Mathematics Education, Reston, Va, v. 31, p. 500 - 507. 2000. KONDRATIEVA, M. F.; RADU, O. Fostering connections between the verbal, algebraic, and geometric representations of basic planar curves for student’s success in the study of mathematics. The Montana Mathematics Enthusiast, USA, v. 6, n. 1-2, p. 213 - 238. 2009. LEINHARDT, G.; ZASLAVSKY, O.; STEIN, M. K. Functions, graphs, and graphing: tasks, learning, and teaching. Review of Educational Research, Washington, US, v. 60, p. 1 - 64. 1990. LLOYD, G. W.; WILSON, M. Supporting innovation: the impact of a teacher’s conceptions of functions on his implementation of a reform curriculum. Journal for Research in Mathematics Education, Reston, Va, v. 29, n. 3, p. 248 - 274. 1998. MARKOVITZ, Z.; EYLON, B.; BRUKHEIMER, M. Functions: Linearity unconstrained. In: INTERNATIONAL CONFERENCE OF THE INTERNATIONALGROUP FOR THE PME, 7th, 1983, Rehovot, Israel. Proceedings… Rehovot, Israel: Weitzman Institute. 1983. p. 271 - 277 (HERSHKOWITZ, R. (Ed.)). MEVARECH, Z. R.; KRAMARSKY, B. From verbal descriptions to graphic representations: stability and change in students’ alternative conceptions. Educational Studies in Mathematics, Dordrecht, Holanda, v. 32, n. 1, p. 229 - 263. 1997. MOSCHKOVICH, J. Moving up and getting steeper: negotiating shared descriptions of linear graphs. The Journal of the Learning Sciences, Mahwah, NJ, v. 5, n. 3, p. 239 - 277. 1996. MOSCHKOVICH, J. Students’ use of the x-intercept as an instance of a transitional conception. Educational Studies in Mathematics, Dordrecht, Holanda, v. 37, p. 169 - 197. 1999. MOSCHKOVICH, J. Appropriating mathematical practice: a case study of learning to use and explore functions through interaction with a tutor. Educational Studies in Mathematics Dordrecht, Holanda, v. 55, p. 49 - 80. 2004. NATHAN, M. J.; KIM, S. Pattern generalization with graphs and words: a cross- sectional and longitudinal analysis of middle school students’ representational fluency. Mathematical Thinking and Learning, England, v. 9, n. 3, p. 193 - 219. 2007. NCTM. Principles and standards for school mathematics. VA: Reston. 2000. NEMIROVSKY, R. On mathematical visualization and the place where we live. Educational Studies in Mathematics, Dordrecht, Holanda, v. 33, p. 99 - 131. 1997. NOSS, R.; BAKI, A. Liberating school mathematics from procedural view. Journal of Education Hacettepe University, Turkey, v. 12, p. 179 - 182. 1996. ORTON, A. Understanding rate of change. Mathematics in School, London, GB, v. 13, n. 5, p. 23 - 26. 1984. PADILLA, M.; MCKENZIE, D. L.; SHAW, E. L. An examination of the line graphing ability of students in grades seven through twelve. School Science and Mathematics, Menasha, Wis., US, v. 86, p. 20 - 26. 1986. RIDER, R. L. Using the SOLO taxonomy to evaluate student learning of function concepts in developmental algebra. In: NORTH AMERICAN CHAPTER OF THE INTERNATIONAL GROUP FOR THE PSYCHOLOGY OF MATHEMATICSEDUCATION, 2004, Toronto, Canada. Proceeding…Toronto, Canada: Ontario Institute for Studies in Education of University of Toronto. 2004. RIZZITU, J. M. Students’ conceptualizations of mathematics functions: the effect of a pedagogical approach involving multiple representations.1991. Thesis (Doctoral in Mathematics Education) - Cornell University, Ithaca, NY, 1991. (52-10A, 3549). SCHOENFELD, A. H.; SMITH, J. P.; ARCAVI, A. Learning: the microgenetic analysis of one student’s evolving understanding of a complex subject matter domain. In: GLASER, R. (Ed.), Advances in instructional psychology. Hillsdale, NJ: Lawrence Erlbaum. 1993. p. 55 - 175, v. 4. SHERIN, M. G. When teaching becomes learning. Cognition and Instruction, Mahwah, NJ, v. 20, n. 2, p. 119 - 150. 2002 SMITH, J.; ARCAVI, A.; SCHOENFELD, A. H. Learning y-intercept: assembling the pieces of an atomic concept. In: INTERNATIONAL CONFERENCE ON THE PSYCHOLOGY OF MATHEMATICS, 13th, 1989, Paris. Proceedings… Paris, France: International Group for the Psychology of Mathematics Education.1989. p. 174 - 181,v. 3. STRAUSS, A.; CORBIN, J. Basics of qualitative research: Grounded theory procedures and techniques. London: Sage. 1990. STUMP, S. L. Secondary mathematics teachers’ knowledge of the concept of slope.1996. Thesis (Doctoral in… area of doctoral) - Illinois State University, Illinois. 1996. STUMP, S. L. High school precalculus students’ understanding of slope as measure.School Science and Mathematics, Menasha, Wis., US, v. 101, p. 81 - 89. 2001 ZASLAVSKY, O.; SELA, H.; LERON, U. Being sloppy about slope: the effect of changing the scale. Educational Studies in Mathematics, Dordrecht, Holanda, v. 49, p. 119 - 140. 2002.